Which answer could be the result of two complex conjugates being multiplied together?(1 point)%0D%0AResponses%0D%0A%0D%0A9−9i%0D%0A9 minus 9 i%0D%0A%0D%0A25+4i%0D%0A25 plus 4 i%0D%0A%0D%0A20%0D%0A20%0D%0A%0D%0A16i

Answer 1

The product of two complex conjugates \(a + bi\) and \(a - bi\) is given by the formula:

\[ (a + bi)(a - bi) = a^2 - (bi)^2 = a^2 + b^2 \]

This results in a real number since the imaginary part cancels out. Therefore, the result must not have any imaginary component.

Now let's analyze the provided options:

1. \(9 - 9i\) - This is not a real number (it has an imaginary part).
2. \(25 + 4i\) - This is also not a real number.
3. \(20\) - This is a real number; could be the result of multiplying two complex conjugates.
4. \(16i\) - This is not a real number (it has an imaginary part).

The only option that can be the result of multiplying two complex conjugates is:

20.